I'm looking for some data on the endangerment of Southwestern Mandarin.
Since it is rather a broad subject, it can be broken down to the Cheng–Yu 成渝 branch as it is quite representative of the language family.
Though Sichuanese is not as endangered as some other languages of China, the prevalence of Sichuanese has dramatically lessened as the popularity of Standard Chinese has risen.
The endangerment claim cites:
"四川经验：剽悍方言无需要保卫" (in Chinese). 新浪网新民周刊专题. Retrieved 2010-05-15.
Which links to this article: 四川经验：剽悍方言无需要保卫(图), an entertainment piece which doesn't say much of anything.
《20世纪成都话银边研究》by 周及徐 has some interesting information on the evolution of pronunciations that clearly show the language being heavily influenced by Standard Mandarin, but it doesn't talk about endangerment.